Question 1

What does an exponent count?

Accepted Answer

The exponent counts equal factors. (Tempting mistake: 2³ = 6. Why it feels right: I multiplied the base by the exponent.)

Question 2

If your child says: “Doubling means adding the same amount each time.”

Accepted Answer

Ask: Did the layer count increase by the same amount each time? What’s true: Each increase equals the current amount.

Question 3

If your child says: “Two cubed means two times three.”

Accepted Answer

Ask: Are these twos added or multiplied? What’s true: The exponent counts factors, not additions.

Question 4

If your child says: “Multiplying powers means multiplying their exponents.”

Accepted Answer

Ask: How many factors came from each group? What’s true: When multiplying powers with the same base, keep that base and add the exponents.

Question 5

If your child says: “Multiply the bases and add the exponents.”

Accepted Answer

Ask: How many sixes did the pairing produce? What’s true: Pairing keeps the original number of repetitions.

Question 6

If your child says: “Just add the numbers of choices.”

Accepted Answer

Ask: Does each top get just one bottom, or both? What’s true: Each top can pair with either bottom, so count both outfits for each top.

Question 7

If your child says: “A zero exponent makes zero.”

Accepted Answer

Ask: What remains when each fraction equals one? What’s true: Every nonzero base has zero power equal to one.

Question 8

If your child says: “Any multiplier works in standard form.”

Accepted Answer

Ask: Is your multiplier at least one and below ten? What’s true: An equal value may still need rewriting into standard form.

Question 9

If your child says: “Only the base matters when comparing powers.”

Accepted Answer

Ask: Both bases are ten, so what makes their values different? What’s true: Both the base and exponent affect a power's value.

Power Play: common misconceptions

The tempting mistake & worked visual